#### Document Type

Article

#### Date

4-3-2007

#### Embargo Period

11-28-2011

#### Disciplines

Mathematics

#### Description/Abstract

We show that if a complete Riemannian manifold supports a vector field such that the Ricci tensor plus the Lie derivative of the metric with respect to the vector field has a positive lower bound, then the fundamental group is finite. In particular, it follows that complete shrinking Ricci solitons and complete smooth metric measure spaces with a positive lower bound on the Bakry-Emery tensor have finite fundamental group. The method of proof is to generalize arguments of Garcia-Rio and Fernandez-Lopez in the compact case.

#### Recommended Citation

Wylie, William, "Complete Shrinking Ricci Solitons have Finite Fundamental Group" (2007). *Mathematics Faculty Scholarship.* Paper 125.

http://surface.syr.edu/mat/125

#### Source

Harvested from arXiv.org

## Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/0704.0317